<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:math>type IIA orientifolds
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:math>type IIA orientifolds
We study a $D=4,$ $N=1,$ type IIA orientifold with an orbifold group ${Z}_{N}$ and ${Z}_{N}\ifmmode\times\else\texttimes\fi{}{Z}_{M}.$ We calculate the one-loop vacuum amplitudes for the Klein bottle, cylinder, and M\"obius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the ${Z}_{4},$ ${Z}_{8},$ ${Z}_{8}^{\ensuremath{'}},$ …